Fleming was spotted by secretary/manager Sam Allen, playing for local team St.Marks, and was invited for a trial. It took just one reserve game for Fleming to earn a contract - he scored twice in a 4-0 win over Salisbury. Seven days later, on October 19th, 1907, Fleming made his senior debut versus Luton, scoring one goal, creating two others, and missing a penalty, as the Town won 4-0 again. Fleming finished as top scorer that season, with 17 goals from 30 appearances.

The following season, Fleming scored 28 goals in 34 games, and was rewarded with international honours. To this day, he holds the record for the number of England appearances made by a Swindon player, making eleven appearances in which he scored nine goals, including a hat-trick in a 6-1 win over Ireland in Dublin in 1912.

During his time at Swindon, the team won the Southern League championship twice, and also reached the FA Cup Semi-Finals twice. In the second semi-final, versus Barnsley, Fleming was obviously seen as the dangerman, and he was singled out for some rough treatment. The injuries he sustained kept him out for 10 months. Fleming's career was interrupted again when the first War began, during which time he worked as a PE instructor in Cambridge.

After the war, Fleming returned to Swindon, and when the Town joined the Football League in 1920, Fleming was one of the players who played in the inaugural first match. He struck four goals in the Town's 9-1 win over Luton, which remains the club's record league victory.

Fleming's last game was on 9th April, 1924, when he again scored in a 4-0 win. One of the greatest players in the club's history has been immortalised with a statue that stands in the club's foyer. Also, he has a street in Swindon named after him, Fleming Way.